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Hydrodynamic limit of a disordered lattice gas

A. Faggionato·F. Martinelli
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Abstract

We consider a model of lattice gas dynamics in the d-dimensional cubic lattice in the presence of disorder. If the particle interaction is only mutual exclusion and if the disorder field is given by i.i.d. bounded random variables, we prove the almost sure existence of the hydrodynamical limit in dimension d>2. The limit equation is a non linear diffusion equation with diffusion matrix characterized by a variational principle.

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A. Faggionato, F. Martinelli. 2003-02-11. Hydrodynamic limit of a disordered lattice gas. https://arxiv.org/abs/math/0302123

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